English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the graph isomorphism game that arises in quantum information theoryfrom the perspective of bigalois extensions of compact quantum groups. We showthat every algebraic quantum isomorphism between a pair of (quantum) graphs $X$and $Y$ arises as a quotient of a certain measured bigalois extension for thequantum automorphism groups $G_X$ and $G_Y$ of the graphs $X$ and $Y$. Inparticular, this implies that the quantum groups $G_X$ and $G_Y$ are monoidallyequivalent. We also establish a converse to this result, which says that everycompact quantum group $G$ monoidally equivalent to $G_X$ is of the form $G_Y$for a suitably chosen quantum graph $Y$ that is quantum isomorphic to $X$. Asan application of these results, we deduce that the $\ast$-algebraic,C$^\ast$-algebraic, and quantum commuting (qc) notions of a quantum isomorphismbetween classical graphs $X$ and $Y$ all coincide. Using the notion ofequivalence for non-local games, we deduce the same result for othersynchronous non-local games, including the synBCS game and certain relatedgraph homomorphism games.

Bigalois extensions and the graph isomorphism game